Question

a town has a population of 17000 and grows at 4% every year. what will be the population after 12 years, to the nearest whole number?

Explanation:

Step1: Recall the compound growth formula

The formula for compound growth is \( P(t) = P_0(1 + r)^t \), where \( P_0 \) is the initial population, \( r \) is the growth rate (in decimal), \( t \) is the time in years, and \( P(t) \) is the population after \( t \) years.

Step2: Identify the values

Here, \( P_0 = 17000 \), \( r = 4\% = 0.04 \), and \( t = 12 \).

Step3: Substitute the values into the formula

\( P(12) = 17000(1 + 0.04)^{12} \)

Step4: Calculate \( (1 + 0.04)^{12} \)

First, calculate \( 1.04^{12} \). Using a calculator, \( 1.04^{12} \approx 1.601032218 \)

Step5: Multiply by the initial population

\( P(12) = 17000 \times 1.601032218 \approx 27217.5477 \)

Step6: Round to the nearest whole number

Rounding \( 27217.5477 \) to the nearest whole number gives \( 27218 \).

Answer:

27218